# A Residual Inverse Power Method

 Title A Residual Inverse Power Method Publication Type Reports Year of Publication 2007 Authors Stewart G.W Date Published 2007/02// Institution Instititue for Advanced Computer Studies, Univ of Maryland, College Park Keywords Technical Report Abstract The inverse power method involves solving shifted equations of theform $(A -\sigma I)v = u$. This paper describes a variant method in which shifted equations may be solved to a fixed reduced accuracy without affecting convergence. The idea is to alter the right-hand side to produce a correction step to be added to the current approximations. The digits of this step divide into two parts: leading digits that correct the solution and trailing garbage. Hence the step can be be evaluated to a reduced accuracy corresponding to the correcting digits. The cost is an additional multiplication by $A$ at each step to generate the right-hand side. Analysis and experiments show that the method is suitable for normal and mildly nonnormal problems. URL http://drum.lib.umd.edu/handle/1903/4260